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Abstract
p-i-n photodiodes comprising dense arrays of InGaAs quantum dots (referred to as quantum well-dots) were fabricated, and the basic physical processes affecting their high-speed performance were studied for the first time by measuring the frequency response under illumination with photons absorbed either in the quantum well-dots (905-nm illumination) or mainly in GaAs layers (860-nm illumination). A GaAs p-i-n photodiode of similar design was also measured for comparison. A maximum −3 dB bandwidth of 8.2 GHz was measured for the 905-nm light illumination, and maximum internal −3 dB bandwidth of 12.5 GHz was estimated taking into account the effect of RC-parasitic by the equivalent circuit model. It was found that the internal response is mainly controlled by the carrier drift time in the depletion region; this process can be characterized by a field-dependent effective velocity of charge carriers in the layered heterostructure, which is approximately half the saturation velocity in GaAs. The carrier escape from the InGaAs quantum well-dots was found to has less effect; the escape time was estimated to be 12–17 ps depending on the reverse-bias voltage applied.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Low-dimensional heterostructures made of lattice mismatched materials, such as strained quantum wells (QWs) and self-organized quantum dots (QDs), are known as efficient media for extending the spectral response of various optoelectronic devices beyond the limit set by the bandgap of lattice-matched bulk semiconductors. In particular, InGaAs/GaAs QWs can be designed to emit at 1.2xx µm [1,2], whereas InAs/InGaAs/GaAs QDs allow further extending the optical transition wavelength in structures grown on GaAs substrates to the 1.3 µm spectral interval [3,4]. For various applications, high optical gain (e.g., in high-speed lasers and microlasers) or high absorption coefficient (e.g., in photodiodes and photovoltaic elements) is favorable. However, the accumulation of strain in multilayered nanostructures leads to the formation of structural defects, such as misfit dislocations, that degrades the optical quality upon reaching a critical amount of the lattice mismatched material [5,6]. This restricts the maximum optical gain or absorption, when a particular sort of nanostructures is used. Therefore, it is advantageous to exploit those nanostructures, which are capable of producing high gain/absorption per layer and can be multiply stacked.
In solar cells, additional absorption of longer-wavelength photons by the nanostructures embedded into the matrix layer can provide an improvement of their performance [7,8]. An enhancement of GaAs photocurrent by 1.3 mA/cm2 (AM0) has been reported for 40 x InAs QDs [9] owing to additional light absorption beyond the GaAs absorption edge (>860 nm). Higher increment of the photocurrent, by 4.1 mA/cm2 (AM1.5), has been achieved with 100 x InGaAs/GaAs/GaAsP QWs [10]. Still higher photocurrent increment of 4.6 (5.2) mA/cm2 for AM1.5 (AM0) spectrum has been demonstrated [11] for 20 layers of InGaAs quantum well-dots (QWDs) in a GaAs matrix. Those InGaAs QWDs, which are responsible for appearance of a longer wave spectral response (900–1100 nm), represent an array of three-dimensional islands. Their surface density, which depends to some extent on the chemical composition, effective thickness and growth condition, is primarily determined by the formation of islands at the edges of atoms on a misoriented surface; it is typically in the mid of 1011 cm−2, i.e. an order of magnitude higher as compared to Stranski-Krastanow QDs [12,13]. As a result, InGaAs QWDs provide the highest photocurrent increment per single layer (0.23–0.26 mA/cm2) among the aforementioned nanostructures. Using waveguide structures of different lengths, per-layer modal absorptions of 69 cm−1 and 13 cm−1 for the ground state optical transitions of QWDs and Stranski-Krastanow QDs was estimated [14]. The InGaAs QWDs are also promising for use in edge-emitting lasers, since the modal gain as high as 49 cm−1 per QWD layer was reported [15]. Microdisk lasers with InGaAs QWDs revealed the capability of operation at temperatures above 100°C [16], high-speed optical data transmission [17], and hybrid integration with silicon [18].
Still another prospective application of InGaAs QWDs, which has not been discussed yet, is photodetectors (PDs) operating in the 0.9–1.1 µm spectral range, where the short-wavelength response of InGaAs/InP and the long-wavelength response of GaAs and Si fall down. Meanwhile, lasers and light emitting diodes of this spectral interval are widely used in various applications, which include machine vision systems, biometrics, materials processing, various surgical and aesthetic medical applications, range finding, infra-red illumination, etc. All the above make PDs, in particular high-speed PDs, which are capable of detecting light of this spectral range, in demand. InGaAs/GaAs QW resonant cavity enhanced PD with the peak responsivity at 0.97 µm has shown the maximum −3 dB bandwidth ${f_{ - 3\textrm{dB}}}$ of 1.3 GHz [19]. Using multi-stacked InGaAs/GaAs QDs, resonant-cavity enhanced PDs operating at 1.06 µm [20] and 1.03 µm [21] have been demonstrated. No information on dynamic response was provided. A p-i-n PD grown on a Si substrate with QDs operating at longer wavelengths of 1.3 µm have demonstrated ${f_{ - 3\textrm{dB}}}$ of 5.5 GHz [22]. Very recently, the record-high −3 dB bandwidth of 20 GHz has been reported on for a QD-based avalanche PD heterogeneously integrated with silicon [23].
In this work, InGaAs QWD p-i-n PDs are characterized for the first time in terms of their small-signal modulation frequency response. The highest ${f_{ - 3\textrm{dB}}}$ of 8.2 GHz is experimentally measured and the −3 dB bandwidth of the internal optical-electrical response was extracted to be 12.5 GHz taking into account the parameters of the small-signal equivalent circuit de-embedded from the electrical reflection measurements. The field-dependent effective velocity of charge carriers and the escape times were estimated by comparing the results obtained under illumination by photons with different wavelengths.
2. Experimental
An epitaxial structure was grown on a semi-insulating GaAs substrate by metal-organic vapor phase epitaxy, Fig. 1(a). Upon a 1-µm-thick n++ buffer layer a 0.2-µm-thick n-GaAs cathode region doped with Si at 2×1018 cm−3 was grown followed by a 1.2 µm-thick intrinsic region, in which 20 layers of QWDs were uniformly inserted (after each 56 nm of GaAs), a 0.2-µm-thick anode region doped with Zn at 2×1018 cm−3, a 30-nm-thick p+-AlGaAs window, and a 0.1-µm-thick p++ GaAs cap layer. The substrate was misoriented by 6° off (100) plane to promote transformation of InGaAs thin layers into a dense array of islands, which represents QWDs. The effective thickness of the deposited InGaAs was about 1 nm; an average InAs mole fraction was 40%. The temperature of the active region growth was about 500°C. Round mesas with a diameter of 36 µm and a height of about 1.7 µm were fabricated by dry etching. MnAg/Ni/Au metallization was used to form ring-shaped p contacts with internal diameters of 28 µm; half-ring-shaped n contacts with an indent of 6 µm from the mesa sidewalls were formed using AuGe/Ni/Au metallization (inset to Fig. 1(b)).
Fig. 1. a) Schematic cross-section view; b) dark I-V curve at room temperature. Inset: SEM image of the fabricated device; c) voltage-dependent responsivity at different wavelengths. Inset: room-temperature spectral response at different voltage.
The mesas sidewall and surface outside the photosensitive area were protected with polyimide without any additional surface passivation. Contact pads were coated with 2-µm-thick electroplated gold. A typical current-voltage (I-V) curve measured without light illumination is presented in Fig. 1(b). The dark current was measured about 0.14 nA (current density ∼2×10−5 A/cm2) at a reverse-bias voltage of −1 V. This value is comparable to the dark current densities of QD-based PDs presented in [24,22] (∼8×10−5 A/cm2 and ∼4×10−5 A/cm2, respectively) but is, however, noticeably inferior to the record-low values of ∼3.5×10−7 A/cm2 reported recently in [25,26] for the same reverse-bias condition. It should be noted that the dark current of the QWD PDs under study changes very slightly with increasing reverse-bias voltage and reaches 1.1 nA (∼2×10−4 A/cm2) at −20 V. This is unlike the previously reported behavior of QD-based PDs (e.g., the dark current rose by an order of magnitude as the voltage changes from −1 to −7 V [22]). The higher dark current densities presented here in comparison with the record-low values of QD-based PDs can be explained, at least in part, by the leakage current on the side walls of the mesa, which were not passivated. In photodiodes with a larger area (50×200 µm2), the measured dark current density was an order of magnitude lower showing the potential for further improvement of the QWD PD performance.
The InGaAs QWDs provide absorption of photons with energies below the bandgap of the GaAs matrix. The absorption maximum is typically located at ∼1.1 µm. By varying the composition and effective thickness of InGaAs it is possible to shift it to ∼900…1050 nm interval [27]. In the present work, in order to better match the spectral response of the photodiodes under study with the emission wavelength of an available high-speed laser, the QWD parameters were selected to have the responsivity peak at a wavelength of about 0.96 µm, inset to Fig. 1(c). At this wavelength of the InGaAs QWD absorption, which is associated with electron-heavy hole optical transitions, the internal quantum efficiency reaches about 29%. A shorter-wavelength absorption peak at ∼910 nm is caused by light holes [27,28]. For the sake of comparison, a p-i-n structure without InGaAs QWD insertions, in which the intrinsic region represents a 1-µm-thick layer of undoped GaAs, was also grown and processed into PDs with a similar topology and antireflection coating of the photosensitive area (hereinafter GaAs PD).
A schematic drawing of the experimental setup used for the frequency response measurements is shown in Fig. 2. A vector network analyzer PNA N5234B was used to measure microwave reflection (S22 parameters for PDs) and small-signal modulation response (S21 parameter). Two high-speed In(Al)GaAs/GaAs vertical-cavity surface-emitting lasers (VCSELs) of different wavelengths (860 or 905 nm) were used as sources of optical excitation in determining the optical-electrical (OE) frequency response of the PDs under study. The 860nm-VCSEL was used in the analysis of the conventional GaAs-based PD as well as the InGaAs QWD PD, when it was excited into a GaAs matrix. When the 905nm-range VCSEL was used, the PD response was solely associated with the light absorption by InGaAs QWDs whereas GaAs matrix is transparent. The VCSEL emission was coupled into a multimode optical fiber via a hybrid-integrated macro-lens (to increase the numerical aperture) and detected by high-speed fiber-optic detector (HSFOD) Newport 1414–50. The multimode optical fiber was connected to the light-wave probe with a micro-lens fiber tip positioned in front of the PD under test.
The photocurrent was measured at −5 V reverse bias voltage, which corresponds to a full depletion of the intrinsic region (takes place at about −3.5 V), whereas the leakage current remains below 1 nA. Based on the measurement results, the responsivity of the investigated InGaAs QWD PDs can be estimated at the level of 0.35 A/W and 0.09 A/W for the wavelengths of 860 nm and 905 nm, respectively. These values agree with the spectral response of the InGaAs QWD PD measured in a wide wavelength range with the use of a tungsten lamp and a monochromator, Fig. 1(c). The responsivity of the GaAs PD was estimated to be 0.52 A/W and 0.002 A/W for the wavelengths of 860 nm and 905 nm, respectively. The low sensitivity of the InGaAs QWD PD is partly explained by an incomplete spectral matching with the VCSEL emission as well as by a lower density of states of the active region, which was grown to have the absorption peak below 1 µm. Note that the maximum responsivity of 0.75 A/W was measured in a 200-µm-long waveguide PD with a QWD active region having the maximum absorption at ∼1.1 µm. The responsivity of the InGaAs QWD PD can be further improved by anti-reflection coating of the top surface.
The small-signal modulation characteristics of the VCSELs were measured by the InGaAs QWD PD (S21PD) as well as by the high-speed calibrated detector (S21HSFOD). Examples are presented in Fig. 3(a). After that, the OE response (S21OE) of the InGaAs QWD PD was extracted by subtracting S21HSFOD from S21PD. Figure 3(b) show the S21OE curves of the InGaAs QWD PD measured at different reverse-bias voltages. For both illumination wavelengths, the −3 dB bandwidth is improved from about 6.3–6.4 GHz to 8.2 GHz with the rise of the reverse-bias voltage from −1 V to −5 V.
Fig. 3. a) Small-signal modulation response of 860-nm and 905-nm VCSELs at fixed current (2 mA) measured by calibrated HSFOD detector and InGaAs QWD PD; b) OE response of InGaAs QWD PD illuminated by 860-nm or 905-nm-VCSELs.
To eliminate the influence of RC-parasitic effect and to focus on the inherent processes inside the InGaAs QWD PD, we determined the RC-limited cutoff frequency. The electrical characteristics of the PD can be described by the equivalent circuit presented in the inset to Fig. 4(a). Here IPD is the ideal current source representing the photocurrent generated by PD, Cj - the intrinsic diode capacitance, i.e. the capacitance of the depletion region of the reverse-biased p-i-n structure, Rj - the diode junction resistance, Rs - the series resistance of the contacts and the doped regions of the diode, Rpad, Lpad and Cpad - the pad parasitic resistance, inductivity and capacitance, respectively. These parameters can be obtained from the microwave reflection measured without any laser emission by iterative fitting the simulated curves of microwave reflection for a given equivalent circuit to the experimental data.
Fig. 4. a) Measured (symbols) and fitted (lines) microwave reflection S22 at −5 V and 20°C. Inset: small signal equivalent circuit, the dark current is neglected; b) simulated RC-limited response.
The obtained parameters of the equivalent circuit are presented in the legend of Fig. 4(b). They are very weakly dependent on the reverse-bias voltage applied to the photodiode. The series resistance agrees well with the slope of the I-V curve under forward bias. The Cj is extracted to be 100 fF, which correlates with that of conventional p-i-n GaAs PD having a comparable thickness of the intrinsic region and mesa area [29]. We suggest that relatively high value of Cpad of 80 fF by the simple single-mesa PD geometry, where the heavily doped n+ GaAs layer remains, which, together with the polyimide planarization layer and the anode electrode, forms a parasitic capacitor. The validity of the extracted values of the equivalent circuit parameters can be seen from the good agreement between the modeled and measured S22 curves presented in Fig. 4(a); the deviations in the considered frequency range does not exceed 0.5 GHz. The frequency response of the equivalent circuit model simulated using the extracted parameters is shown in Fig. 4(b). The RC-limited cutoff frequency was found to be about 14 GHz.
The internal OE response was de-embedded from the measured S21OE by subtracting the RC-limited frequency response and, finally, values of the internal −3 dB bandwidth, $f_{ - 3\textrm{dB}}^{\textrm{int}}$, were extracted for different bias voltages. The largest $f_{ - 3\textrm{dB}}^{\textrm{int}}$ of the InGaAs QWD PD illuminated with 905-nm light was found to be 12.5 GHz; it is achieved already at −5 V reverse-bias voltage. In order to clarify the relative contributions of various physical processes affecting the dynamic performance, we estimated the internal OE response for the InGaAs QWD PD illuminated by 860-nm VCSEL, when the incident light is primarily absorbed by the GaAs layers, and for the reference GaAs PD. The results are summarized in Fig. 5(a). It is seen that the $f_{ - 3\textrm{dB}}^{\textrm{int}}$ data taken for the InGaAs PDs under different illumination wavelengths are very close to each other, whereas the GaAs PD is characterized by twice the speed.
Fig. 5. a) −3 dB bandwidth estimated from measured (solid symbols) and internal (open symbols) OE responses of GaAs PD and QWD PD; b) field-dependent velocity extracted from the $f_{ - 3\textrm{dB}}^{\textrm{int}}$ data of GaAs PD and InGaAs QWD PD for various diffusion times. Red line corresponds to v in GaAs [31].
It is usually considered that the internal response speed of a photodiode is primarily limited by the carrier transit time $\tau _{\textrm{drift}}^{} = W/v$, where W is the thickness of undoped GaAs, $v$ – the drift velocity of the charge carriers in the depletion region [30], which in general depends on the velocities of both electrons and holes as well as on distances they have to travel in the electric field. This makes the transit time dependent of the relation, usually not precisely known, between the absorption coefficient and the absorbing layer thickness. Fortunately, in a lightly doped GaAs, the saturated velocities of electrons and holes at high electric fields are very close to each other: ${v_\textrm{e}} \approx $ 9.6 × 106 cm/s vs ${v_\textrm{h}} \approx $ 8.7 × 106 cm/s at 60 kV/cm [31]. We used the mean value, i.e. $v = ({{v_\textrm{e}} + {v_\textrm{h}}} )/2 \approx $ 9.1 × 106 cm/s, which gives of about 11 ps for the GaAs PD at high electric fields. The dynamic characteristics can be additionally affected by the diffusion of nonequilibrium carriers photogenerated in the charge-neutral region because of incomplete light absorption in the depleted region [32]. The combined effect of drift and diffusion processes can be described by the sum of the squares of the corresponding time constants [33]: $\tau _{\textrm{int}}^2 = \tau _{\textrm{drift}}^2 + \tau _{\textrm{diff}}^2$, where $\tau _{\textrm{diff}}^{}$ is the diffusion-related component of the internal response time. The latter is related with the internal −3 dB bandwidth as $f_{ - 3\textrm{dB}}^{\textrm{int}} \cong 0.4/\tau _{\textrm{int}}^{}$, and the factor of about 0.4 is explained in [30]. Figure 5(b) presents the electric field dependence of the velocity extracted from the data on $f_{ - 3\textrm{dB}}^{\textrm{int}}$ for the diffusion time varied. We found that $\tau _{\textrm{diff}}^{}$ of 14 ps provides a good agreement between the extracted values and previously published data on the charge carrier velocity in GaAs in high electric fields. For the InGaAs QWD PD under 860-nm-light illumination, we suggest the same diffusion time as the diode design in both cases is very similar except for the InGaAs QWD active region.
Another phenomenon, which can affect the speed of light-absorbing devices with quantum-sized active region and can be taken into account by means of the time constant $\tau _{\textrm{esc}}^{}$, is the escape of photocarriers out of the quantum-sized active region into the matrix, where they are swept by the electric field [34]. In the case of the GaAs PD, the OE response is entirely related to the absorption of photons in the GaAs matrix, so there is no carrier escape process and $\tau _{\textrm{esc}}^{}$ = 0. Since in the case of the InGaAs QWD PD under 860-nm illumination the carrier escape process is expected to be negligible, one can assume a similar internal bandwidth in both cases. However, as can be seen in Fig. 5(a), the insertion of the InGaAs QWDs into the GaAs light-absorbing layer of p-i-n PD leads to a noticeable decrease in the response bandwidth as compared to the case of the reference GaAs PD. This finding can be described in terms of effective velocity of charge carriers in multilayered region, which is noticeably reduced in comparison with the saturated velocities of electrons and holes in GaAs; the maximum (saturated) effective velocity was found to be ∼4.5 × 106 cm/s, Fig. 5(b).
When analyzing the response time of the InGaAs QWD PD exposed to light of 905-nm wavelength absorbed directly in the InGaAs QWDs, we assumed that the drift time of charge carriers remains unchanged with respect to the case of light of 860-nm wavelength absorbed in the matrix. This allowed us to estimate the escape time of charge carriers under the assumption that the diffusion time is zero, Fig. 6. The escape time decreases from ∼17 ps to less than 12 ps as the reverse-bias voltage increases. Note that for InAs/InGaAs QDs, the escape time of the hole of ∼30 ps was calculated and confirmed by modelling the frequency response of QD photodiode [24]. Shortening the escape time of both electrons and holes in high electric field has been previously demonstrated for quantum wells as a result of fastening the tunneling escape and, in lesser extent, the thermionic emission escape [34,35]. For self-organized quantum dots, a model [36] which describes the hole emission process via thermally activated tunneling through the wetting layer as an intermediate state, predicts the exponential dependence of the escape time on the field, as ${\tau _{\textrm{esc}}} \approx {\tau _1}\textrm{exp}({{F_0}/F} )$, where ${F_0}$ is a parameter that depends on the hole mass and the energy of the optimal intermediate state for the subsequent tunneling process, ${\tau _1}$ is the escape time at an infinitely high electric field strength. Since QWD is a sort of a quantum dot, we believe that the above model will also applicable to describe the escape time in the case of QWDs. The data presented in Fig. 6 can be fitted under the assumption of tunneling of one type of carriers with ${\tau _1}$=10 ps and ${F_0}$=12 kV/cm. We believe that the escape time is mainly limited by holes because of their heavier effective mass; however, additional experiments are still required to study the peculiarities of the QWD energy level structure and the carrier escape processes in InGaAs QWDs, which is can be different from that of Stranski-Krastanow InAs/InGaAs QDs.
Fig. 6. Internal response time (squares) of QWD PD illuminated with 905-nm light and its components, drift time for effective velocity (triangles) and escape time (circles) as a function of electric field. Dotted line is fit by the model [36].
In conclusion, the high-speed characteristics of infrared p-i-n photodiodes with dense arrays of InGaAs islands (quantum well-dots) were studied. The InGaAs QWDs have revealed their ability to act as an active region of high-speed photodetectors operating in the spectral range lying outside the absorption band of GaAs. We found that the escape of photogenerated carriers out of the InGaAs QWDs can be described by the characteristic time, which drops down to ∼12 ps at sufficiently high electric fields (> 60 kV/cm). In addition to the equivalent circuit parasites, that reduce the −3dB bandwidth from its internal value of 12.5 GHz down to experimentally measured one of 8.2 GHz, carrier drift in the intrinsic region has the greatest impact on the dynamic performance. We found that the drift time increases approximately twice, i. e. the effective drift velocity is nearly halved, in the photodiode with multiply stacked InGaAs QWDs compared to that in the reference p-i-n diode with purely GaAs absorbing layer. To our best knowledge, this effect has been previously discussed neither for multi-QW nor multi-QD structures.
Funding
National Research University Higher School of Economics (Basic Research Program); Russian Science Foundation (18-12-00287, https://rscf.ru/project/18-12-00287/).
Acknowledgments
This work was supported by the Russian Science Foundation (grant # 18-12-00287, https://rscf.ru/project/18-12-00287/). Support of optical measurements from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged. The authors are thankful to N. N. Ledentsov (VI Systems) for the 905-nm-VCSEL provided. SEM characterization was fulfilled at the Center for Collective Use of the Ioffe Institute.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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